Consider the geometric sequence $3$, $\dfrac{9}{2}$, $\dfrac{27}{4}$, $\dfrac{81}{8}$, $\ldots$. Find the eighth term of the sequence.  Express your answer as a common fraction.
Explanation: The first term is $3$, and the ratio between terms is $(9/2)/3=3/2$. Therefore, the eighth term of the sequence is $3\cdot(3/2)^{8-1} = 3^8/2^7 = \boxed{\frac{6561}{128}}$.